Smith - Debreu : social Interaction and Mathematical Metaphors. Origin and conclusion of the Principal Scientific Research Project in Economic Theory

This paper provides evidence for the assertion that there is deep structural coherence between the work of Adam Smith and modern general equilibrium theory, most notably Gérard Debreu's Theory of Value. In particular, we show that Adam Smith formulated a number of highly original and to some extent quite stringent assumptions about the structure of human interaction that ultimately allow the establishment of a generalized market economy with a maximization of private as well as social benefits. The discussion focuses on the following issues: (a) methodology, (b) commodities, compactness and codification, (c) constant returns to scale, (d) convexity in preferences and (e) the invisible hand and Kakutani's fixed point theorem.